Integration-free Kernels for Equivariant Gaussian Process Modelling
Authors: Tim Steinert, David Ginsbourger, August Lykke-Møller, Ove Christiansen, Henry Moss
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We now present a series of experiments designed to highlight the advantages of incorporating equivariances in GP models, alongside the specific benefits of our integrationfree equivariant kernel. First, we model equivariant velocity fields, comparing with the popular Helmholtz kernel, which exhibits equivariance only in the posterior mean. Next, we consider a challenging real-world test case involving the prediction of molecular dipole moments, demonstrating the enhanced uncertainty quantification and practical applicability of our proposed kernel. Finally, we explore the efficacy of our GP models in a parameter estimation problem disentangling a real-world ocean velocity dataset from equivariant perturbations. |
| Researcher Affiliation | Academia | 1IMSV, University of Bern, Switzerland 2Department of Chemistry, University of Aarhus, Denmark 3School of Mathematical Sciences, Lancaster University, UK 4Department of Applied Maths and Theoretical Physics, University of Cambridge, UK. Correspondence to: <EMAIL>. |
| Pseudocode | No | The paper describes methods and theoretical frameworks but does not include any explicitly labeled pseudocode or algorithm blocks. Procedures are explained in narrative text. |
| Open Source Code | Yes | We provide the dipole moment data from Section 5.2 along with a notebook containing the code necessary to reproduce the experiments in this Github repository. |
| Open Datasets | Yes | F Ref represents ocean drifter velocities on a set of 564 locations in the Gulf of Mexico, as taken from the Gulf Drifters Open dataset Lilly & P erez-Brunius (2021) |
| Dataset Splits | Yes | Data generation To assess the predictive performance of a zero-mean rotation-equivariant GP with our proposed integration-free kernel, we build a dataset of n noisy measurements Dn = {(xi, yi)}n i=1, with yi given as realisations of F (xi) + εi, εi N(0, σ2 obs I2) for two synthetic SO(2)-equivariant vector fields F 1(x) = ( x(2), x(1)), x [ 1, 1]2, F 2(x) = x 0.5 + x 4 , x [ 2, 2]2, with n = 8, 10 observations and σobs = 0.15, 0.1 for F 1 and F 2, respectively. See Appendix A.3 for a detailed explanation of the training and evaluation procedure. |
| Hardware Specification | Yes | All computations in this paper were performed on a cluster equipped with singlecore AMD EPYC2 CPUs running at a clock time of 2.25 GHz. With a straightforward implementation, the difference in computation time for moderate training and test set sizes is considerable. While computing the posterior distribution of GP(0, KR ) at 500 test locations given 100 training points requires 45 hours, with GP(0, Kπ) it takes a total of 55 seconds. |
| Software Dependencies | Yes | Christiansen, O., Artiukhin, D. G., Bader, F. D., Godtliebsen, I. H., Gras, E. M., Gy orffy, W., Hansen, M. B., Hansen, M. B., Højlund, M. G., Høyer, N. M., Jensen, A. B., Klinting, E. L., Kongsted, J., K onig, C., Madsen, D., Madsen, N. K., Monrad, K., Schmitz, G., Seidler, P., Sneskov, K., Sparta, M., Thomsen, B., Toffoli, D., and Zoccante, A. Midascpp, version 2024.04.0, 2024. |
| Experiment Setup | Yes | For experiment 5.1, the optimization is run for 1000 iterations with a learning rate of 0.01, starting from the initial values θinit = (1, 1, 1, 1, 0.1). |